Inequalities and Quantum Entanglement

From the Cauchy-Schwarz Inequality to Non-linear Entanglement Witnesses

Bachelor Thesis (2019)
Author(s)

S.M. Loor (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Contributor(s)

J Vermeer – Mentor (TU Delft - Analysis)

D. Elkouss – Mentor (TU Delft - Quantum Information and Software)

C Vuik – Graduation committee member (TU Delft - Numerical Analysis)

Tim H. Taminiau – Graduation committee member (TU Delft - QID/Taminiau Lab)

Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright
© 2019 Stephan Loor
More Info
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Publication Year
2019
Language
English
Copyright
© 2019 Stephan Loor
Graduation Date
31-07-2019
Awarding Institution
Delft University of Technology
Programme
Applied Mathematics | Applied Physics
Faculty
Electrical Engineering, Mathematics and Computer Science
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Abstract

In this thesis, two topics are studied: mathematical inequalities and non-linear quantum entanglement witnesses. First, various inequalities, like the Cauchy-Schwarz inequality (on finite dimensional vector spaces) and Jensen's inequality, along with their extensions and generalisations, are proved and discussed. The intimate relationship between these inequalities is studied. Because this thesis was restricted to finite dimensional vector spaces, the consequences of generalising the results to infinite dimensional vector spaces are finally determined. Secondly, the topic of entanglement detection is discussed - specifically, non-linear entanglement witnesses are considered. A bipartite and multipartite entanglement criterion based on the previously discussed inequalities are introduced and assessed extensively by considering their optimality, how they relate to other criteria as well as their limitations.

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